Finite Group Databasebeta

← #28401338

Subgroups — #28401338

Order 14464.

472 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299108C211yesmaximal, characteristic, complemented
2C2×#16813597C211yesmaximal, characteristic, complemented
3#20298933C211yesmaximal, characteristic, complemented
4#20298924C212yesmaximal, complemented
5#20298833C212yesmaximal, complemented
6#20298828C212yesmaximal, complemented
7#20298751C211yesmaximal, characteristic, complemented
8#20298744C212yesmaximal, complemented
9#20298731C211yesmaximal, characteristic, complemented
10C22⋊C8×D113C211yesmaximal, characteristic, complemented
11#481×C113C211yesmaximal, characteristic, complemented
12C2×#14268646C2211yescharacteristic, complemented
13C22×D452—21no—
14C22×D452C2211yescharacteristic
15C22×C4×D113C2211yescharacteristic
16C2×#14268636C2212yescomplemented
17C2×#14268632C2212yescomplemented
18C2×C8×D113C2212yescomplemented
19#16813604—21no—
20#16813602C2211yescharacteristic, complemented
21#16813601C2211yescharacteristic
22#16813597—21no—
23#16813597—21no—
24#16813597C2212yes—
25#16813597C2212yes—
26#16813593C2211yescharacteristic, complemented
27#16813590—21no—
28D4×Dic113—21no—
29#16813582—21no—
30#16813580C2211yescharacteristic, complemented
31C2×#14268624—21no—
32#16813555C2212yescomplemented
33#16813545C2212yescomplemented
34#16813544C2212yescomplemented
35#16813542C2212yescomplemented
36C22⋊#11744751C2211yescharacteristic
37#16813534C2212yescomplemented
38#121×C113C2211yescharacteristic
39C2×C4⋊C4×C113C2211yescharacteristic
40#106×C113C2212yescomplemented
41#102×C113C2212yescomplemented
42C22⋊C8×C113C2211yescharacteristic
43C23×D113—21no—
44C23×D113D411yescharacteristic
45#14268646—42no—
46C2×Dic226C2311yescharacteristic
47C2×D452—22no—
48C2×D452—22no—
49C2×D452—21no—
50C2×D452—42no—
51C2×D452—44no—
52C2×D452C2312yes—
53C2×C22⋊D113—21no—
54C2×C22⋊D113—21no—
55C22×Dic113—21no—
56C22×Dic113D411yescharacteristic
57C2×C4×D113—42no—
58C2×C4×D113D411yescharacteristic
59C2×C4×D113D411yescharacteristic
60C2×C4×D113C2311yescharacteristic
61C2×C4×D113C2311yescharacteristic
62#14268636—42no—
63#14268632—42no—
64C2×#11744751C2312yes—
65C8×D113—42no—
66C4⋊Dic113—21no—
67C4⋊Dic113C2311yescharacteristic
68#14268626—21no—
69C22⋊Dic113—21no—
70C22⋊Dic113—21no—
71#14268624—21no—
72#14268624—21no—
73#14268624—22no—
74#14268624—22no—
75C4×Dic113—21no—
76C2×D4×C113—21no—
77C2×D4×C113C2311yescharacteristic
78C22×C4×C113—21no—
79C22×C4×C113C2311yescharacteristic
80C2×C8×C113C2312yes—
81C4⋊C4×C113—21no—
82C4⋊C4×C113C2311yescharacteristic
83C4⋊C4×C113C2312yes—
84C22⋊C4×C113—21no—
85C23×C113—21no—
86C23×C113C2×D411yescharacteristic
87C22×D113—22no—
88C22×D113—22no—
89C22×D113—22no—
90C22×D113—41no—
91C22×D113—42no—
92C22×D113—42no—
93C22×D113—42no—
94C22×D113C2×D411yescharacteristic
95C22×D113C2×D411yescharacteristic
96D4×C113—22no—
97D4×C113—42no—
98C2×C4×C113—22no—
99C2×C4×C113—21no—
100C2×C4×C113—22no—
101C2×C4×C113—42no—
102C2×C4×C113C2×D411yescharacteristic
103C2×C4×C113C2411yescharacteristic
104C22⋊D113—42no—
105C22⋊D113—42no—
106C2×Dic113—21no—
107C2×Dic113—21no—
108C2×Dic113—41no—
109C2×Dic113—42no—
110C2×Dic113C2×D411yescharacteristic
111C2×Dic113C2×D411yescharacteristic
112D452—22no—
113D452—22no—
114D452—42no—
115D452—44no—
116D452—44no—
117C4×D113—22no—
118C4×D113—22no—
119C4×D113—41no—
120C4×D113—41no—
121Dic226—22no—
122C8×C113—22no—
123#11744751—22no—
124C22×C113—21no—
125C22×C113—21no—
126C22×C113—41no—
127C22×C113—41no—
128C22×C113—41no—
129C22×C113#13512yes—
130C22×C113C22×D411yescharacteristic
131C2×D113—21no—
132C2×D113—21no—
133C2×D113—21no—
134C2×D113—21no—
135C2×D113—21no—
136C2×D113—44no—
137C2×D113—42no—
138C2×D113—42no—
139C2×D113—42no—
140C2×D113—84no—
141C2×D113AGL(1,ℤ/8)12yes—
142C4×C113—21no—
143C4×C113—41no—
144C4×C113—42no—
145C4×C113H(5,𝔽2)12yes—
146Dic113—21no—
147Dic113—21no—
148Dic113—41no—
149Dic113—41no—
150C2×C113—22no—
151C2×C113—81no—
152C2×C113#53411yescharacteristic
153C2×C113C2×#13511yescharacteristic
154C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
155D113—22no—
156D113—41no—
157D113—82no—
158#3188—1131nomaximal, Sylow
159C113#318811yescharacteristic, complemented, Sylow
160#525—1131no—
161C2×#121—1131no—
162#484—1131no—
163#482—1132no—
164#481D11311yescharacteristic, complemented
165#466—1132no—
166#465—1132no—
167#450—1131no—
168#449—1132no—
169#447—1131no—
170C2×C22⋊C8—1131no—
171C2×#41—1131no—
172C22×D4—1131no—
173C22×D4—2261no—
174C23×C4—1131no—
175C2×SD16—1132no—
176C2×D8—1132no—
177C22×C8—1132no—
178#123—2261no—
179C22⋊Q8—1131no—
180C22⋊Q8—1131no—
181#121—1131no—
182#121—1132no—
183#121—1132no—
184#121—2261no—
185#121—2261no—
186#121C2×D11311yescharacteristic
187#120—2261no—
188C4×D4—2261no—
189C4×D4—2261no—
190#117—1131no—
191C2×C4⋊C4C2×D11311yescharacteristic
192C2×C22⋊C4—2261no—
193#107—1132no—
194#106C2×D11312yescomplemented
195#103—1132no—
196#102—1132no—
197#102—1132no—
198#102C2×D11312yescomplemented
199C22⋊C8—1131no—
200C22⋊C8—1132no—
201C22⋊C8C2×D11311yescharacteristic
202C24—1131no—
203C24—2261no—
204#41—4522no—
205C2×Q8—1131no—
206C2×D4—21no—
207C2×D4—1132no—
208C2×D4—4522no—
209C2×D4—4524no—
210C2×D4—2262no—
211C2×D4—2262no—
212C2×D4—2261no—
213C2×D4—2261no—
214C2×D4—2261no—
215C2×D4C22×D11311yescharacteristic
216C22×C4—21no—
217C22×C4—1131no—
218C22×C4—1131no—
219C22×C4—1131no—
220C22×C4—1131no—
221C22×C4—1131no—
222C22×C4—4522no—
223C22×C4—2261no—
224C22×C4C22×D11311yescharacteristic
225SD16—4522no—
226D8—4522no—
227C2×C8—1132no—
228C2×C8—4522no—
229C2×C8C22×D11312yes—
230C4⋊C4—21no—
231C4⋊C4—1131no—
232C4⋊C4—2261no—
233C4⋊C4—2261no—
234C4⋊C4C22×D11311yescharacteristic
235C4⋊C4C22×D11312yes—
236C22⋊C4—21no—
237C22⋊C4—2262no—
238C22⋊C4—2262no—
239C22⋊C4—2261no—
240C22⋊C4—2261no—
241C22⋊C4—2261no—
242C22⋊C4—2261no—
243C42—2261no—
244C23—21no—
245C23—1131no—
246C23—1131no—
247C23—4522no—
248C23—4522no—
249C23—4521no—
250C23—4522no—
251C23—2262no—
252C23—2262no—
253C23—2262no—
254C23D4×D11311yescharacteristic
255Q8—2262no—
256D4—22no—
257D4—42no—
258D4—4522no—
259D4—4524no—
260D4—4524no—
261D4—4522no—
262D4—4522no—
263D4—2262no—
264D4—2262no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—42no—
269C2×C4—1131no—
270C2×C4—1131no—
271C2×C4—4521no—
272C2×C4—4521no—
273C2×C4—4522no—
274C2×C4—4521no—
275C2×C4—2261no—
276C2×C4—2261no—
277C2×C4—2262no—
278C2×C4—2262no—
279C2×C4D4×D11311yescharacteristic
280C2×C4C23×D11311yescharacteristic
281C8—22no—
282C8—2262no—
283C22—21no—
284C22—21no—
285C22—41no—
286C22—41no—
287C22—41no—
288C22—1132no—
289C22—9044no—
290C22—4524no—
291C22—4522no—
292C22—4522no—
293C22—4522no—
294C22—2261no—
295C22—2261no—
296C22—2261no—
297C22—2261no—
298C22—2261no—
299C22#1681364312yes—
300C22C2×D4×D11311yescharacteristic
301C4—21no—
302C4—41no—
303C4—42no—
304C4—4521no—
305C4—4521no—
306C4—2261no—
307C4—2261no—
308C4#1681366812yes—
309C2—22no—
310C2—81no—
311C2—9042no—
312C2—4521no—
313C2—2262no—
314C2#2029915911yescharacteristic
315C2C2×#1681364311yescharacteristic
316C2AGL(1,ℤ/8)×D11311yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#481×C113C2
socleC22×C113C22×D4
hypercenter#481D113
hypocenterC113#3188
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20299108C2semidirect
2. C2×#16813597C2semidirect
3. #20298933C2semidirect
4. #20298924C2semidirect
5. #20298833C2semidirect
6. #20298828C2semidirect
7. #20298751C2semidirect
8. #20298744C2semidirect
9. #20298731C2semidirect
10. C22⋊C8×D113C2semidirect
11. #481×C113C2semidirect
12. C2×#14268646C22semidirect
16. C2×#14268636C22semidirect
17. C2×#14268632C22semidirect
18. C2×C8×D113C22semidirect
20. #16813602C22semidirect
26. #16813593C22semidirect
30. #16813580C22semidirect
32. #16813555C22semidirect
33. #16813545C22semidirect
34. #16813544C22semidirect
35. #16813542C22semidirect
37. #16813534C22semidirect
40. #106×C113C22semidirect
41. #102×C113C22semidirect
159. C113#3188semidirect
164. #481D113semidirect
194. #106C2×D113semidirect
198. #102C2×D113semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202991082
C2×#168135972
#202989332
#202989242
#202988332
#202988282
#202987512
#202987442
#202987312
C22⋊C8×D1132
#481×C1132
#3188113